office: Evans 775

Department of Mathematics

University of California, Berkeley

970 Evans Hall

Berkeley, CA 94720

LEC 001: Evans 10, MWF 3-4

office hours: M 11:30-12:30, F 2-3, or by appointment

a short survey for the first day of class, and an evaluation for the middle of the semester

We will use the third edition of *Precalculus: A Prelude to Calculus* by Sheldon Axler.

Homework will be due (in person) at the beginning of discussion on the days listed in the schedule below. Late homework will not be accepted. Quizzes will occur during discussion and will cover the textbook sections indicated in the schedule below. Problems will be similar to those on the homework.

If you cannot attend my office hours, please give me a list of times when you are free so we can schedule a meeting.

More information is included in the syllabus. You can also use this form to send me a question or comment anonymously. (Berkeley login required.)

Visit the SLC for information about the adjunct course, tutoring, and other services.

GSI | office hours | discussion sections |
---|---|---|

Nafisa Arain | Evans 858 | DIS 101: Evans 4, MW 8-9 |

Tu 4-5, Th 12:30-1:30 | DIS 102: Latimer 121, MW 9-10 | |

Scott Mutchnik | Evans 832 | DIS 103: Latimer 122, MW 9-10 |

F 11-1 | DIS 105: Evans 4, MW 10-11 | |

Emily Bain | Evans 1049 | DIS 104: Evans 2, MW 10-11 |

Tu 12-2 | DIS 106: Latimer 121, MW 11-12 | |

Madeline Brandt | Evans 1065 | DIS 107: Dwinelle 79, MW 11-12 |

F 10-12 | DIS 108: Dwinelle 79, MW 12-1 | |

Theresa Honein | Evans 858 | DIS 109: Evans 5, MW 1-2 |

M 12-1, W 2-3 | DIS 110: Dwinelle 130, MW 8-9 |

hw 1 | 0.2: 6-52 evens; 53,55 | scan |
---|---|---|

0.3: 2-28 evens; 75-79 all | scan | |

hw 2 | 0.3: 32-36,42-46,58-62 evens; 64-65,69-71 all | sol 0 |

1.1: 2-26,34-46 evens; 62,68 | ||

hw 3 | 1.2: 6-28 evens; 51-53 all | |

1.3: 4-60 multiples of 4; 71 | ||

1.4: 2-14,22-26,40-46 evens; 65-66 all | ||

hw 4 | 1.5: 2-24,34 evens; 39,43-44 all | |

1.6: 2-14 evens; 39-41,44 all | sol 1 | |

2.1: 4,10-16,26-36,42-44 evens; 47,57-58 all | ||

hw 5 | 2.2: 14-24,36-40 evens; 48-60,76-80 multiples of 4; 99 | |

2.4: 4-28 multiples of 4; 33,35,43,49-50 all | ||

2.5: 2-12,28-32,36-42 evens; 47 | ||

hw 6 | 2.3: 4-20,28-56,80-100 multiples of 4; 120-122 all | sol 2 |

3.1: 8-36,56-76 multiples of 4; 85,90-92 all | ||

hw 7 | 3.2: 4-8,46-48 evens; 50,52-54,56 all | |

3.3: 12-34 evens; 59-67 all | ||

hw 8 | 3.5: 8-22,38-50 evens | |

3.7: 2-16,26-28 evens; 36 | sol 3 | |

4.2: 2-24,32,36-38,42-46 evens; 51 | ||

hw 9 | 4.3: 2-6,12-24 evens; 35-38 all | |

4.4: 8-20 evens; 24-40 multiples of 4; 43-45 | ||

4.5: 2-4,10-30 evens; 43 | rev 4 | |

hw 10 | 5.1: 2-10,18-20,26-30,36,42-48 evens; 55-56 all | |

4.6: 8-72 multiples of 4; 74,88,90 all | ||

hw 11 | 5.2: 4-12,20-28,36-40 multiples of 4; 43-50 all | |

5.4: 4-8,12-24 evens; 26,28,30-32 all | ||

5.5: 12-56,64-68 multiples of 4; 74 | ||

hw 12 | 5.6: 6-36 evens | |

5.7: 2-32 evens |

8/28 | 0.2 | algebra | |

8/30 | 0.3 | absolute values | |

9/2 | NO CLASS | ||

9/4 | 0.3 | inequalities | hw 1 due |

9/6 | 1.1 | functions | |

9/9 | 1.2 | graphs | quiz 0.2-0.3 |

9/11 | 1.3 | transformations | hw 2 due |

9/13 | 1.4 | composition | |

9/16 | 1.5 | inverses | quiz 0.3-1.2 |

9/18 | 1.6 | more graphs | hw 3 due |

9/20 | 2.1 | lines | |

9/23 | 2.2 | conics | quiz 1.3-1.5 |

9/25 | 2.4 | polynomials | hw 4 due |

9/27 | 2.5 | rational functions | |

9/30 | extra time | quiz 1.6-2.2 | |

10/2 | review | ||

10/4 | EXAM | ||

10/7 | 2.3 | exponents | |

10/9 | CLASS CANCELED | ||

10/11 | CLASS CANCELED | ||

10/14 | 3.1 | logarithms | quiz 2.4-2.5, hw 5 due |

10/16 | 3.2 | power rule | hw 6 due |

10/18 | 3.3 | product and quotient rules | |

10/21 | 3.5 | e and ln | quiz 2.3,3.1 |

10/23 | 3.7 | exponential growth | hw 7 due |

10/25 | 4.2 | radians | |

10/28 | CLASS CANCELED | ||

10/30 | 4.3 | cosine and sine | quiz 3.2-3.3,3.5, hw 8 due |

4.4 | tangent, etc. [remote lecture] | ||

11/1 | 4.5 | right triangles | |

11/4 | 5.1 | inverse trig. functions | quiz 3.7,4.2-4.3 |

11/6 | review | ||

11/8 | EXAM | ||

11/11 | NO CLASS | ||

11/13 | 4.6 | identities | hw 9 due |

11/15 | 5.2 | more identities | |

11/18 | 5.4 | laws of sines and cosines | quiz 4.5-4.6,5.1 |

11/20 | 5.5 | double- and half-angle formulas | hw 10 due |

11/22 | 5.6 | addition and subtraction formulas | |

11/25 | 5.7 | more transformations | hw 11 due |

11/27 | NO CLASS | ||

11/29 | NO CLASS | ||

12/2 | extra time | quiz 5.4-5.6 | |

12/4 | extra time | hw 12 due | |

12/6 | review | ||

12/17 | FINAL 7-10 pm (location TBD) |

Consider the rings k[s^2,st] and k[s^2,t^2]. What are their dimensions? Are they integrally closed? How do they relate to maps to projective space?

How about k[s^3,s^2t,st^2,t^3]?

Calculate a Grobner basis for for the ideal (xz,yw,xw) in k[x,y,z,w].

Give the Koszul complex on the generators of this ideal. Is it a resolution?

Define the canonical curve of genus 4 and describe its ideal sheaf.

Find the Picard group of a nonsingular quadric.

Draw a picture of Spec Z[x].

What are the maximal ideals in the ring of smooth functions on a compact manifold?

Define the tangent space.

Given a vector field X, do there exist local coordinates under which X is constant?